There are several implications for teaching informal inference; however, they all have an over-arching theme that informal inference needs to be introduced early and revisited across several grade levels (Zieffler, Garfield, delMas, & Reading, 2008). In order to develop students’ conceptual understanding of informal inference, teachers should be thoughtful and intentional about their selection of tasks they use in their classroom (Ben-Zvi, 2006; Paparistodemou & Meletiou-Mavrotheris, 2008; Zieffler et al., 2008; Garfield & Ben-Zvi, 2008; Garfield & Ben-Zvi, 2007; Stohl & Tarr, 2002). These tasks need to be appropriate for the grade level and where students are in their development of informal inference skills. Research also suggests that teachers should select tasks that are data-driven and open-ended and focus on analyzing and drawing conclusions in context (Rossman & Chance, 1999; Garfield & Ben-Zvi, 2008; Paparistodemou & Meletiou-Mavrotheris, 2008; Tarr, Lee, & Rider, 2006; Rossman, 2008). This context should transition from personal contexts to more external contexts as students progress through the developmental stages of inferential reasoning.
Many researchers promote the incorporation of technology into classroom lessons in general. Technology in statistical lessons allows students to explore data quickly and create multiple representations, which provides more time to analyze the data and draw richer inferences (Rossman & Chance, 1999; Ben-Zvi, 2006; Paparistodemou & Meletiou-Mavrotheris, 2008; Stohl & Tarr, 2002; Tarr et al., 2006; Wild, Pfannkuch, Regan, & Horton, 2011). Technology also allows students to explore data open-ended to draw their own conclusions instead of a recipe-based approach that dictates the inferences the students will draw from a task.
References Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics. [CDROM]. Voorburg, The Netherlands: International Statistical Institute.
Garfield, J,. & Ben-Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International Statistical Review. 75(3), 372-396.
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. New York: Springer.
Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Developing young students’ informal inference skills in data analysis. Statistics Education Research Journal, 7(2). 83-106.
Rossman, A. J. (2008). Reasoning about informal statistical inference: One statistician’s view.Statistics Education Research Journal, 7(2). 5-19.
Rossman, A. J., & Chance, B. L. (1999). Teaching the reasoning of statistical inference: A "top ten" list. The College Mathematics Journal, 30(4), 297-305.
Stohl, H. & Tarr, J. E. (2002). Developing notions of inference using probability simulation tools. Journal of Mathematical Behavior, 21, 319-337.
Tarr, J. E., Stohl Lee, H., & Rider, R. (2006). When data and chance collide: Drawing inferences from simulation data. In G. F. Burrill & P. C. Elliott (Eds.), Thinking and reasoning with data and chance: Sixty-eighth NCTM yearbook (pp. 139-150). Reston, VA: National Council of Teachers of Mathematics.
Wild, C. J., Pfannkuch, M., Regan, M., & Horton, N. J. (2011). Towards more accessible conceptions of statistical inference. Journal of the Royal Statistical Society. Series A, 174(2), 247-295.
Zieffler, A., Garfield, J., delMas, R., & Reading, C. (2008). A framework to support research on informal inferential reasoning.Statistics Education Research Journal, 7(2), 40-58.
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Five Tasks
1. Guess Your Question
2. Are you a Sleeping Sheep or a Turbo-charged Cheetah?
3. M&M Activity
4. Which Brand Should I Buy?
5. Movies and Sleep Habits
Implications for Teaching
There are several implications for teaching informal inference; however, they all have an over-arching theme that informal inference needs to be introduced early and revisited across several grade levels (Zieffler, Garfield, delMas, & Reading, 2008). In order to develop students’ conceptual understanding of informal inference, teachers should be thoughtful and intentional about their selection of tasks they use in their classroom (Ben-Zvi, 2006; Paparistodemou & Meletiou-Mavrotheris, 2008; Zieffler et al., 2008; Garfield & Ben-Zvi, 2008; Garfield & Ben-Zvi, 2007; Stohl & Tarr, 2002). These tasks need to be appropriate for the grade level and where students are in their development of informal inference skills. Research also suggests that teachers should select tasks that are data-driven and open-ended and focus on analyzing and drawing conclusions in context (Rossman & Chance, 1999; Garfield & Ben-Zvi, 2008; Paparistodemou & Meletiou-Mavrotheris, 2008; Tarr, Lee, & Rider, 2006; Rossman, 2008). This context should transition from personal contexts to more external contexts as students progress through the developmental stages of inferential reasoning.
Many researchers promote the incorporation of technology into classroom lessons in general. Technology in statistical lessons allows students to explore data quickly and create multiple representations, which provides more time to analyze the data and draw richer inferences (Rossman & Chance, 1999; Ben-Zvi, 2006; Paparistodemou & Meletiou-Mavrotheris, 2008; Stohl & Tarr, 2002; Tarr et al., 2006; Wild, Pfannkuch, Regan, & Horton, 2011). Technology also allows students to explore data open-ended to draw their own conclusions instead of a recipe-based approach that dictates the inferences the students will draw from a task.
References
Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics. [CDROM]. Voorburg, The Netherlands: International Statistical Institute.
Garfield, J,. & Ben-Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International Statistical Review. 75(3), 372-396.
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. New York: Springer.
Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Developing young students’ informal inference skills in data analysis. Statistics Education Research Journal, 7(2). 83-106.
Rossman, A. J. (2008). Reasoning about informal statistical inference: One statistician’s view.Statistics Education Research Journal, 7(2). 5-19.
Rossman, A. J., & Chance, B. L. (1999). Teaching the reasoning of statistical inference: A "top ten" list. The College Mathematics Journal, 30(4), 297-305.
Stohl, H. & Tarr, J. E. (2002). Developing notions of inference using probability simulation tools. Journal of Mathematical Behavior, 21, 319-337.
Tarr, J. E., Stohl Lee, H., & Rider, R. (2006). When data and chance collide: Drawing inferences from simulation data. In G. F. Burrill & P. C. Elliott (Eds.), Thinking and reasoning with data and chance: Sixty-eighth NCTM yearbook (pp. 139-150). Reston, VA: National Council of Teachers of Mathematics.
Wild, C. J., Pfannkuch, M., Regan, M., & Horton, N. J. (2011). Towards more accessible conceptions of statistical inference. Journal of the Royal Statistical Society. Series A, 174(2), 247-295.
Zieffler, A., Garfield, J., delMas, R., & Reading, C. (2008). A framework to support research on informal inferential reasoning.Statistics Education Research Journal, 7(2), 40-58.